Question

The parallel axis theorem relates icm, the moment of inertia of an object about an axis passing through its center of mass, to ip, the moment of inertia of the same object about a parallel axis passing through point p. What is the mathematical statement of the theorem?

1) ip = icm * md²
2) ip = icm / md²
3) ip = icm + md²
4) ip = icm - md²

Answer 1

The parallel axis theorem states that the moment of inertia about a parallel axis (Ip) is equal to the moment of inertia about a center of mass axis (Icm) plus the product of the mass (m) and the square of the distance (d^2) between the two axes.

Step-by-step explanation:

The parallel axis theorem is a principle in physics that relates the moment of inertia of an object about an axis passing through its center of mass (Icm) to the moment of inertia about a parallel axis (Ip) that is not through its center of mass. The mathematical statement of this theorem is:

Ip = Icm + md2

Here, m represents the mass of the object and d is the perpendicular distance from the center of mass axis to the new axis. The theorem shows that the moment of inertia about the parallel axis is always greater than the moment about the center of mass axis by the quantity md2.